Work

Analysis of Time‐Harmonic Electromagnetic Problems With Elliptic Material Coefficients

Year: 2025

Type: article

Abstract: ABSTRACT We consider time‐harmonic electromagnetic problems with material coefficients represented by elliptic fields, covering a wide range of complex and anisotropic material media. The properties of elliptic fields are analyzed, with particular emphasis on scalar fields and normal tensor fields. Time‐harmonic electromagnetic problems with general elliptic material fields are then studied. Well‐posedness results for classical variational formulations with different boundary conditions are reviewed, and hypotheses for the coercivity of the corresponding sesquilinear forms are investigated. Finally, the proposed framework is applied to examples of media used in the literature, such as isotropic lossy media, cloaks of invisibility, magnetized ferrites, and cold plasmas.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70318

Authors: Patrick Ciarlet, Axel Modave

Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, École Nationale Supérieure de Techniques Avancées, Institut Polytechnique de Paris, POEMS: Propagation des Ondes : Etude Mathématique et Simulationan

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Agence de l'innovation de Défense

Award: Wave-Specific Discontinuous Galerkin Finite Element Methods for Time-Harmonic Problems